Evolution of wide O star binaries through their LBV stage. Population synthesis with mass-ejection-driven orbital evolution

Abstract

Context. Long-period Wolf-Rayet (WR) star binaries produced by mass transfer are predicted to be abundant, but are observationally rare. This yields constraints on the evolution of initially wide O star binaries, including those potentially leading to the formation of gravitational-wave sources through the Common Envelope Channel. Aims. We investigate this issue in the light of a new type of orbital evolution for initially wide O star binaries, which is driven by mass ejection at periastron passage during the Luminous Blue Variable (LBV) phase. Methods. The assumption that the mass ejection occurs instantly at periastron passage allows us to analytically describe the orbital evolution. This approach is motivated by our understanding of an Eddington-limit driven LBV phase. We perform population synthesis calculations for the WR stars in the Small Magellanic Cloud (SMC), and compare them to the observed SMC WR star population. Results. Different from mass transfer, our mass ejection scenario leads to increased orbital periods and eccentricities. The Galactic system WR 140 (orbital period 2895 d, eccentricity 0.9) could be a typical result of this evolution scenario. Our models predict measurable binary space velocities, and allow for the disruption of the binary. Our SMC population synthesis model predicts statistically 5.3 close, 3.7 long-period, and further 2 runaway single WR stars. With largely increased orbital periods and eccentricities, such WR+O star binaries may not be ruled out by past radial-velocity searches. Applying our scenario to the Gaia BH1 and BH2 systems, we find that it provides viable progenitor evolution models. Conclusions. The mass-ejection-driven orbital evolution could explain why so few wide WR binaries are observed, and why some of the apparently single WR stars have high space velocities. We discuss implications for gravitational-wave sources.

Figures (12)

• Figure 1: Schematic evolutionary sequence for forming merging black holes through common envelope evolution from isolated massive binaries. The meaning of the abbreviations are, 1) "ZAMS" for zero-age main sequence, 2) "RLO" for Roche-lobe overflow, 3) "He" for helium star, 4) "OB" for OB-type main-sequence star, 5) "CEE" for common envelope evolution, 6) "GW" for gravitational wave. Cumulating evidence shows that the progenitors (indicated by the red box) of the CEE phase are rarer than expected in recent surveys.
• Figure 2: Comparison between our fitting formula (blue curve; Eq. \ref{['eq:Ie-fit']}) and the numerical solution of Eq. \ref{['eq:Ie']} (orange curve). The black solid and dashed lines represent $I(1)=\pi/2$ and $I(0)=1$.
• Figure 3: Example models using the mass-ejection-driven orbital evolution, assuming that the primary star ejects a mass of $10^{-3}\,M_\odot$ during each periastron passage. The two columns correspond to two initial eccentricities, 0.0 (left) and 0.3 (right). From top to bottom, the panels present the evolution of orbital period, eccentricity, the velocity of the centre of mass, and the average orbital velocity of the mass-losing star. Each panel contains three curves, computed with different initial orbital periods, 10 d (solid line), 100 d (dashed line), and 1000 d (dotted line). The markers correspond to ejected masses of $25\%M_{\rm b,0}$ (circle), $37.5\%\,M_\odot$ (square), and $\Delta M_{\rm dis}$ (Eq. \ref{['dm_per_disr']}; diamond). In the $\langle\upsilon_{\rm s1}\rangle$ panel, we use coloured regions to indicate the ranges of the orbital velocities of the mass-losing stars of different initial orbital periods (blue: 10 d; brown: $10^2$ d; green: $10^3\,$d), where the upper and lower limits are determined by the velocities at periastron (Eq. \ref{['eq:v-s1-per']}) and apastron (Eq. \ref{['eq:v-s1-ap']}). The red star means that the mass-losing star ejects half of its initial mass. The dashed lines mark $P_{\rm orb}=10^4\,$d (assumed detection limit), $e=0.9$Thomas2021, and $\upsilon_{\rm CoM}=80\,\mathrm{km\,s}^{-1}$Schootemeijer2024.
• Figure 4: Inferred properties of the progenitor of WR 140 as a function of the pre-mass-ejection eccentricity. Panel (a) presents the inferred mass ejection fraction, which is the mass of the hydrogen-rich envelope of the primary star divided by the pre-mass-ejection binary mass. Panel (b) presents the inferred pre-mass-ejection mass of the WR progenitor, using the BPASS model Thomas2021 and the MESA model Jin2024AA...690A.135JJin2025, respectively, for comparison. Panel (c) presents the pre-mass-ejection orbital period. Panel (d) presents the predicted current velocity of the centre of mass, where the grey region indicates the observed proper motion of WR 140 Dzib2009RMxAA..45....3D.
• Figure 5: Population synthesis predictions with a fixed initial eccentricity, 0.4. The upper-left panel presents the predicted orbital period distribution, where the systems formed through the mass-transfer- and mass-ejection-driven orbital evolution are plotted in blue and orange, respectively, and the text indicates the predicted numbers. The vertical dashed line marks the longest orbital period (20 d) of the observed WR+O binaries in the SMC. The prediction by Simulation2, which is the fiducial model in Xu2025AA...704A.218X but with a higher star formation rate, is plotted in grey for comparison. The 2D distributions are the mass-ejection WR+O population on the eccentricity-$\,\mathrm{log}\,P_\mathrm{orb}$ (upper-right), -$\upsilon_{\rm CoM}$ (middle-left) and -$\langle\upsilon_{\rm s1}\rangle$ (middle-right) planes, where the predicted number in each pixel is colour-coded. The third row presents the predicted distributions of WR star masses ($M_{\rm WR}$) and mass ratios (WR star/O star) of the mass-ejection WR+O binaries. The bottom panel presents the predicted space velocities of the runaway WR stars.